Representative Martin J. Walsh and City Councilor John R. Connolly jousted tonight over a recent negative turn in the Boston mayoral campaign, during their last major televised debate, which comes with the race tightening and the election only a week away.

“We had tens of thousands of fliers mailed which savagely attacked me and my family,” said Connolly, saying the fliers were “filled with lies.”

Walsh said he had asked union groups sending out the fliers to stop and countercharged that Connolly had conducted “push polling” — a campaign technique in which people pretend to be conducting a poll to spread negative information about an opposing candidate.

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“This was an attack on me in certain parts of the city of Boston,” he said. Connolly denied that any push polling had taken place.

The two candidates also tangled again on Walsh’s ties to unions. Walsh has worked as a union official while serving in the State House and pushed for a decade for legislation that would eliminate the requirement that the City Council approve arbitration awards for police and firefighters. Under his proposal, arbitration rulings would be final.

Attention to the issue has been heightened by a recent arbitrator’s ruling that called for an increase in Boston police salaries that city officials say would amount to a 25.4 percent hike over six years.

“You haven’t been independent in your role as a state representative. How are you going to be independent as a mayor?” Connolly asked.

Walsh said he was proud of organized labor, recalling his father’s work as a laborer and the help his family got from the union when Walsh was a young boy stricken with cancer. But Walsh said he could also be independent from the unions.

“I certainly have expressed many times on this trail my independence from organized labor,” he said. “I am proud of who I support ... but I also know that I can stand up to them when I have to.”

Connolly also argued that Walsh’s legislation eliminating City Council approval for an arbitrator’s award would “compromise the fiscal health of the city,” forcing the city to drop other programs in order to fund the contract.

“That’s why this matters at the end of the day. You are filing bills that would damage the fiscal health of the city,” Connolly said.

But Walsh — who has criticized the arbitrator’s award but has stopped short of asking the City Council to reject it — asserted that he would be able to negotiate contracts with unions before the two sides reach an impasse.

In a veiled shot at Connolly, who is a lawyer, he said, “We don’t need another lawyer in City Hall right now, watching our purse strings in the city of Boston. ... Let me be clear: I will be able to get to a negotiation because of the experience I have, because I have trust on the other side of the table.”

The debate touched on a variety of other issues, including what the candidates would look for when they fill the posts of school superintendent and police commissioner, bilingual programs in the schools, charter schools, and gentrification.

While the two men’s exchanges were tense on some issues, neither took the bait when moderator R.D. Sahl asked them why the other man was not a good candidate for mayor.

“Because of my record and my accomplishments,” said Walsh.

“I think Representative Walsh is qualified to be mayor and I think he’s got a great record of service. I just happen to think that mine is better,” Connolly said.

Both campaigns said Monday that the race, the most competitive in years, is tied, with Walsh seizing momentum in recent weeks after a string of endorsements that included many of Boston’s black and Latino elected officials.

The winner in the Nov. 5 final election will succeed long-time Mayor Thomas M. Menino, who, after suffering a series of ailments, decided not to seek a sixth term, despite his love for the city and the job.

No matter who wins, the city will return to the tradition of having an Irish-American mayor, which had been broken by the 20-year reign of Menino, an Italian-American.

The hourlong debate was held in the studios of WHDH-TV (Channel 7), with former news anchor Sahl moderating.

With the Red Sox taking tonight off from their quest to win the World Series, the debate was expected to draw more attention from voters.

The debate was sponsored by the Boston Media Consortium and aired on the channels of all consortium members, making it the most widely broadcast of the campaign’s three major televised debates.